finance report

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RESEARCH REPORT
ON
OPTIMISATION OF PORTFOLIO RISK AND RETURN
SUBMITTED TO
Dr. A.P.J. ABDUL KALAM TECHNICAL UNIVERSITY
For the partial fulfillment of the requirement of
Master Of Business Administration
Session 2016-17
Under the supervision of: Submitted By:
Dr. PRABHAT DWIVEDI GARGI RAI
ASSISTANT PROFESSOR MBA 4th Sem. AKTU
Roll No.:-1518170031
Science & Technology Entrepreneur Park-Harcourt Butler Technological
Institute, Kanpur,
U.P.- 208002
(Affiliated to APJ ABDUL KALAM TECHNICAL UNIVERSITY, Lucknow)
Formerly known as Uttar Pradesh technical University

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DECLARATION
I hereby declare that the topic of the research report is “FUTURES AND OPTIONS”
which has been prepared under the supervision of Dr. PRABHAT DWIVEDI towards the
partial fulfillment of the requirement of MASTER OF BUSINESS ADMINISTRATION.
This research report has not been submitted to any other university for the award of any
degree or diploma.
(Dr. Prabhat Dwivedi) (Dr. Asheesh Trivedi)
Supervisor O/Incharge MBA Programme
(Prof. R.K. Trivedi)
Director

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ACKNOWLEDGEMENT
The presentation of this research report has given me an opportunity to express my
profound gratitude to all concern in guiding me. Foremost I would like to thank Prof. R.K.
Trivedi the Director of our College, STEP-HBTI for providing an opportunity to undergo
a research study program. I would like to thank Dr. PRABHAT DWIVEDI for guiding
me to complete the research work.
(Dr. Prabhat Dwivedi) (Dr. Asheesh Trivedi)
Supervisor O/Incharge MBA Programme
(Prof. R.K. Trivedi)
Director

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CONTENTS
PART A : * Introduction
: * Objective of Study
: * Methodology
: * Limitations
PART B : * Portfolio and
Holding period returns `
Sharpe’s Performance Measure
Treynor’s Performance Measure
PART C : * Analysis and Interpretations
: * Conclusion & Suggestions
: * Bibliography

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PART A

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INTRODUCTION
Combination of individual assets or securities is a portfolio. Portfolio includes investment
in different types of marketable securities or investment papers like shares, debentures
stock and bonds etc., from different companies or institution held by individuals firms or
corporate units and portfolio management refers to managing securities. Portfolio
management is a complex process and has the following seven broad phases.
1. Specification of investment objectives and constraints.
2. Choice of asset mix.
3. Formulation of portfolio strategy.
4. Selection of securities.
5. Portfolio execution.
6. Portfolio rebalancing.
7. Portfolio performance.

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Portfolio Diversification:
An important way to reduce the risk of investing is to diversify your investments.
Diversification is akin to “not putting all your eggs in one basket”. For example, if your
portfolio only consisted of stocks of technology companies. It would likely face a
substantial loss in value if a major event adversely affected the technology industry.
There are different ways to diversify a portfolio whose holding are concentrated
in one industry. You might invest in the stocks of companies belonging to other industry
groups. You might allocate to different categories of stocks, such as growth, value, or
income stocks. You might include bonds and cash investments in your asset allocation
decisions. Potential bond categories include government, agency municipal and corporate
bonds. You might also diversity by investing in foreign stocks and bonds.
Diversification requires you to invest din securities whose investment returns do
not move together. In other words, their investment returns have a low correlation. The
correlation coefficient is used to measure the degree that returns of two securities are
related. For example, two stocks whose returns move in lockstep have a coefficient of
+1.0. Two stocks whose returns move in exactly the opposite direction have a correlation
of -1.0. To effectively diversity, you should aim to find investments that have a low or
negative correlation.

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As you increase the number of securities in your portfolio, you reach a point
where you’ve likely diversified as much as reasonably possible. Financial planners vary
in their views on how many securities you need to have a fully diversified portfolio.
Some say it is 10 to 20 securities. Others say it is closer to 30 securities. Mutual funds
offer diversification at a lower cost. You can buy no-load mutual funds from an online
broker. Often, you can buy shares fund directly from the mutual fund, avoiding a
commission altogether.

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Asset allocation:
Asset allocation is the process of spreading your investment across the three
major asset classes of stocks, bonds and cash.
Asset allocation is a very important part of your investment decision-making.
Professional financial planner frequently point out that asset allocation decisions are
responsible for must of your investment return.
Asset allocation begins with setting up an initial allocation. First, you should
determine your investment profile. Specially, this requires you to assess you investment
horizon, risk tolerance, and financial goals:
Investment horizon, Also called time horizon your investment horizon is the
number of years you to save for a financial goal. Since you’re likely to have more than
goal, this means you will have more than one investment horizon. For example, saving
for your give-year-daughter’s college has an investment horizon of 12 years. Saving for
your retirement in 30 tears has an investment horizon of 30 years. When you retire, you
will want to have saved a lump sum that is large enough to generate earnings every year
until you die risk tolerance.
Your risk tolerance is a measure of your willingness to accept a higher degree of
risk in exchange for the chance to earn a higher rate or return. This is called the risk-

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return trade-off. Some of us, naturally, are consevatyi9ve investor, while other are
aggressive investors.
As a general rule, the younger your are, the higher your risk tolerance and the
more aggressive you can be. As a result, you can afford to allocate a higher percentage of
your investment to securities with more risk. These include aggressive growth stocks and
the mutual funds that invest ion them.
A more aggressive allocation is viable because you have more time to recover
form a poor year of invest6ment returns.
Financial goal, younger and aggressive investor’s allocation, as a general rule,
younger and aggressive investors allocate 70% to 100% of their portfolios to stocks, with
the remainder in bonds and cash. Conservative investors allocate 40% to 60% in bonds,
and the remainder in cash.
Moderate investors allocate somewhere between the allocation of aggressive and
conservative, to make an initial allocation, you need to build a portfolio of individual
securities, mutual funds, or both. In general, mutual funds provide more diversification
benefit for the buck.
How you choose to precisely allocate among the major asset classes depends, in
part, on other factors. For example, if example, if interest rates are expected to rise, you
might allocate a greater percentage to money market mutual funds, CDs, or other bank
deposits. If rates are headed lower, you may choose to allocate more to stocks or bonds.
Financial planners suggest that you rebalance, or reallocate, your portfolio from
time to time. They differ in their views on how often you should reallocate. It may be
once a year or it may be every three to six months. At a minimum, reallocation lets you
up date any changes in your investment profile, or to take advantage of a change in
interest rates. Rebalancing often involves nothing more than a “fine-tuning” of your

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current6 allocations. For example, a conservative investor may decide to shift 5% of her
portfolio form stocks to cash to take advantage of higher rates that money market funds
may be offering.
-Need
-Objective
-Methodology
SPECIFIC INVESTMENT OBJECTIVE AND
CONSTRAINS
The first step in the portfolio management process is to specify the one’s
investment objectives and constraints.
The commonly stated investment goals are:-
INCOME - To provide a steady income through the regular interest or divided payment.
GROWTH -To increase the value of the principal amount through capital appreciation.
STABILITY – Since income and growth represent two ways by which return is
generated and investment objectives may be expressed in terms of return and risk. An
investor will be interested in higher return and lower level risk. However the risk and
return go hand to hand, so an investor has to bear a higher level of risk in order to earn a
higher return.

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CONSTRAINTS –
An investor should bear in mind the constraints arising our of the following factor.
-Liquidity
-Taxes
-Time horizon
-Unique preferences and circumstances
OBJECTIVES
To construct three portfolios of public sector units, public limited companies and
foreign collaboration and fine their ex-post returns and risk for the period of three year.
To make a comparative study of the risk-adjusted measure of portfolio
performance using the shapre’s and Treynor’s performance indeed under total risk and
market risk and market risk situations, by taking ex-post returns for a period of three
years.

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METHODOLOGY
Using a model consisting of two modules has carried out the work. The first
module involves the section of portfolio and the second module involved evaluation of
portfolio’s performance.
MODULE-1
Securities selection and portfolio construction has been made by taking scripts
Public Sector Units, public limited companies and foreign collaboration units. Equal
weigtage has been given to industries like shipping, oil&gas and power growth oriented
industries like pharmaceuticals, banking and FMCG and technology oriented industries
like software and telecommunications.
MODULE – 2

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Portfolio performance was evaluated by ranking holding period’s returns under
total risk and market risk situation (measured by standard deviation and Beta coefficient)
for the period of three years.
LIMITATIONS
The work has been carried out under the following limitations:
 The all portfolio consist of riskly assets there no risk-free assets.
 Riskly assets consist of equity shares and where as risk-free assets consists of
investments in the saving bank account, deposits, treasury bills, bonds etc.
 The holding period for risky assets was for I yr i.e. shares were assumed to be
purchased at the first day and sold at the second consecutive day and average
return for I yr is considered.
 An equal no of shares i.e. I (one) share of each script is assumed to be purchased
form the secondary market.
 Return on the saving bank account is considered as benchmark rate of return.
 All the portfolio has been held constant for the whole period of the three years.

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PART B

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PORTFOLIOS
PORTFOLIOS I
COMPANIES NSE CODE
BANK OF INDA BANKINDIA
BHEL HEL
HLL HINDLEVER
M&M M&M
SCI SCI
SATYAM COMPUTER SATYAMCOMPUTER
VSNL VSNL
GLAXO GLAXO
IBP IBP
SAIL SAIL

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PORTFOLIO II
COMPANIES NSE CODE
UTI BANK UTIBANK
TATA POWER TATAPOWER
ITC ITC
ESCORTS ESCORTS
VARUNSHIPING VARUNSHIP
WIPRO WIPRO
BHRATI BHRATI
DRREDDYS DRREDDY
IPCL IPCL
TISCL TISCO

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PORTFOLIO III
COMPANIES NSE CODE
ING VYSYA VYSYA BANK
ABB ABB
CADILA CADILA
MICO BOSH MICO
GESHIPPING GESHIP
HUGHES SOFTWARE HUGHESSOFT
TATA TELECOM TATA TELECOM
NICOLAS PHARMA NICOLASPIR
ONGC ONGC
ESSAR STEEL ESSARGUJ

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HOLDING PERIODSRETURNS:
All the investment is made at a certain period of time. Holding period returns
enables an investor to know his returns during that period of time. It can be computed by
using the formula:-
Holding period returns (HPR) =
Today’s closing price – Yesterday’s closing price
Yesterday’s closing price
Holding period returns are used for comparative criterion. Holding period returns
can be compared for making an assessment of relative returns.

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MODULE I

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HOLDING PERIOD
RETURNS
Portfolio I for 2014-15
Name of the
script
Face
value
Dividen
d
declare
d
Dividen
d
amount
Market
price
when
purchase
d
%Return
on
dividend
%Return
on
security
Total
return
BANK OF INDIA 10 0 0 10.5 0 -17.42 -17.42
BHEL 10 40 4 128.7 3.11 40.62 43.729
HLL 1 300 3 222.2 1.35 5.84 7.1901
M&M 10 0 0 119.2 0.00 8.11 8.11
SCI 10 0 0 30.0 0.00 98.11 98.11
SATYAM COMP 2 0 0 243.7 0.00 41.24 41.24
VSNL 10 0 0 286.2 0.00 -20.27 -20.27
GLAXO 10 0 7 417.8 1.68 -3.18 -1.504
IBP 10 100 10 294.3 3.40 119.95 123.35
SAIL 10 0 0 5.7 0.00 -3.98 -3.98
Return 27.855

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Portfolio I for 2015-16
Name of the
script
Face
value
Dividen
d
declare
d
Dividen
d
amount
Market
price
when
purchase
d
%Return
on
dividend
%Return
on
security
Total
return
BANK OF INDIA 10 30 3 26.5 11.32 89.32 100.6
BHEL 10 40 4 180.8 2.21 24.99 27.2
HLL 1 300 3 227.25 1.32 -39.47 -38.14
M&M 10 55 5.5 112.8 4.88 -6.52 -1.644
SCI 10 0 0 72.55 6.00 -20.9 -20.9
SATYAM COMP 2 110 2.2 257 0.86 -28.55 -27.69
VSNL 10 85 8.5 188.5 4.51 -88.61 -84.1
GLAXO 10 70 7 34.7 2.04 -6.5 -4.457
IBP 10 140 14 891.35 1.57 -13.95 -12.38
SAIL 10 0 0 5.65 0.00 71.74 71.74
Return 1.026

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Portfrolio I for 2016-17
Name of the
script
Face
value
Dividen
d
declare
d
Dividen
d
amount
Market
price
when
purchase
d
%Return
on
dividend
%Return
on
security
Total
return
BANK OF INDIA 10 10 1 39.35 2.541 49.06 51.601
BHEL 10 30 3 223.65 1.341 107.1 108.44
HLL 1 300 3 149.15 2.011 8.43 10.441
M&M 10 90 9 99.1 9.082 164.23 173.31
SCI 10 0 0 51.25 0.000 109.51 109.51
SATYAM COMP 2 140 2.8 173.65 1.612 67.29 68.902
VSNL 10 45 45.5 74.3 6.057 59.51 65.567
GLAXO 10 100 10 294.7 3.393 77.02 80.413
IBP 10 0 0 199.8 0.000 123.8 123.8
SAIL 10 0 0 9.05 0.000 153.06 153.0
Return 94.505

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PORTFOLIO II FOR 2014-15
Name of the
script
Face
value
Dividen
d
declare
d
Dividen
d
amount
Market
price
when
purchase
d
%Return
on
dividend
%Return
on
security
Total
return
UTIBANK 10 0 0 23.7 0.000 63.82 63.82
TATAPOWER 10 0 0 103.1 0.000 18.92 18.92
ITC 10 0 0 625 0.000 -10.19 -10.19
ESORTS 10 10 1 77.1 1.297 -10.17 -8.873
VARUNSHIPING 10 0 0 11.55 0.000 6.63 6.63
WIPRO 2 50 1 1268.45 0.079 58.71 58.789
BHARTI 10 0 0 44.35 0.000 -13.12 -13.12
DRREDDY 5 0 0 914.95 0.000 22.24 22.24
IPCI 10 0 0 54.15 0.000 52.26 52.26
TISCO 10 0 0 115.75 0.000 -7.8 -7.8
Return 18.268

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PORTFOLIO II FOR 2015-16
Name of the
script
Face
value
Dividen
d
declare
d
Dividen
d
amount
Market
price
when
purchase
d
%Return
on
dividend
%Return
on
security
Total
return
UTIBANK 10 22 2.2 40.7 5.40541 2.23 7.6354
TATAPOWER 10 65 6.5 114.05 5.69925 2.27 7.9693
ITC 10 0 0 706.3 0 -8.61 -8.61
ESORTS 10 10 1 61.15 1.63532 -48.74 -
47.105
VARUNSHIPING 10 0 0 11.7 0 -21.4 -21.4
WIPRO 2 50 1 1690 0.05917 -22.58 -
22.521
BHARTI 10 20 2 38.9 5.14139 -23.04 -
17.899
DRREDDY 5 100 5 1096.1 0.45616 -13.5 -
13.044
IPCI 10 22.5 2.25 87.5 2.57143 8.47 11.041
TISCO 10 80 8 97.85 8.17578 35.9 44.076

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Return -5.9856
PORTFOLIO II FOR 2016-17
Name of the
script
Face
value
Dividen
d
declare
d
Dividen
d
amount
Market
price
when
purchase
d
%Return
on
dividend
%Return
on
security
Total
return
UTIBANK 10 25 2.5 39.9 6.26566 150.6 156.83
TATAPOWER 10 70 7 114.1 6.13497 128.11 134.24
ITC 10 200 20 625.9 3.1954 54.68 57.875
ESORTS 10 0 0 35.25 0 76.54 76.54
VARUNSHIPING 10 6 0.6 9.2 6.52174 105.49 112.01
WIPRO 2 200 4 1231.2 0.32489 21.35 21.675
BHARTI 10 60 6 29.1 20.6186 183.36 203.98
DRREDDY 5 100 5 914.95 0.54648 14.92 15.466
IPCI 10 25 2.5 83.85 2.98151 89.2 92.182
TISCO 10 100 10 135.1 7.40192 112.82 120.22
Return 99.102

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PORT6FOLIO III FOR 2014-15
Name of the
script
Face
value
Dividen
d
declare
d
Dividen
d
amount
Market
price
when
purchase
d
%Return
on
dividend
%Return
on
security
Total
return
ING VYSA 10 35 3.5 112.2 3.11943 89.95 93.069
ABB 10 0 0 238.9 0 16.72 16.72
CADILA 5 0 0 124 0 11.282 11.28
MICOBOSH 100 0 0 2709 0 -4.06 -4.06
GESHIPPING 10 0 0 25.3 0 22.45 22.45
HUGHES 5 40 2 593.25 0.33713 -40.45 -
40.113
TATATELECOM 10 0 0 56.4 0 139.1 139.1
NICOLAS
PHARMA
10 0 0 295.75 0 -0.047 -0.047
ONGC 10 140 14 125.65 11.1421 87.97 99.112
ESSAR STEEL 10 0 0 125.65 0 87.97 87.97
Return 42.548

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PORTFOLIO III FOR 2015-16
Name of the
script
Face
value
Dividen
d
declare
d
Dividen
d
amount
Market
price
when
purchase
d
%Return
on
dividend
%Return
on
security
Total
return
ING VYSA 10 40 3.5 247.25 1.41557 4.77 6.1856
ABB 10 60 6 263.9 2.27359 12.77 15.044
CADILA 5 70 3.5 129.55 2.70166 -3.31 -
0.6083
MICOBOSH 100 40 40 2387.35 1.6755 47.45 49.125
GESHIPPING 10 40 4 30.75 13.008 25.99 38.998
HUGHES 5 40 2 277.7 0.7202 -28.22 -27.5
TATATELECOM 10 25 2.5 171.9 1.45433 47.45 48.904
NICOLAS
PHARMA
10 105 10.5 271.05 3.87382 -24.88 -
21.006
ONGC 10 130 13 329.6 3.94417 13.43 17.374
ESSAR STEEL 10 0 0 329.6 0 13.43 13.43
Return 13.995

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PORTFOLIO III FOR 2016-17
Name of the
script
Face
value
Dividen
d
declare
d
Dividen
d
amount
Market
price
when
purchase
d
%Return
on
dividend
%Return
on
security
Total
return
ING VYSA 10 40 3.5 247.25 1.41557 76.28 77.696
ABB 10 60 6 263.9 2.27359 106.67 108.94
CADILA 5 70 3.5 129.55 2.70166 144.09 146.04
MICOBOSH 100 40 40 2387.35 1.6755 138.36 140.04
GESHIPPING 10 40 4 30.75 13.0081 135.6 148.61
HUGHES 5 40 2 277.7 0.7202 117.65 118.37
TATATELECOM 10 25 2.5 171.9 1.45433 96.37 97.824
NICOLAS
PHARMA
10 105 10.5 271.05 3.87382 -24.88 -
21.006
ONGC 10 130 13 329.6 3.94417 95.26 99.204
ESSAR STEEL 10 0 0 329.6 0 95.26 95.26
Return 101.1727

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EX-POST PORTFOLIO RETURNS
YEAR PORTFOLIO PORTFOLIO PORTFOLIO
I II III
2005 27.85 18.26 42.54
2006 1.02 -5.98 13.99
2007 94.5 99.1 101.17
Ri 41.1233333 37.12666667 52.567

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MODULE –
II

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RISK ADJUSTED MEASUREMENT OF PORTFOLIO PERFORMANCE
SHARPE’S PERFORMANCE MEASURE
CALCULATIONS OF STANDARD DEVIATION

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Risk
Risk in holding securities is generally associated with the possibility that realized
return will be less than returns were expected. The source of such disappointment is the
failure of dividends or the fail in security’s prices. Forces that contribute to variation in
return, price or dividend const6itures elements of risk. Some influences that are external
to the firm, cannot be controlled and affect large number of securities. Other influences
are internal to the firm are controllable to all large degree.
Systematic Risk
The systematic risk affects the entire market.
Those forces that are uncontrollable external and board in the effect are called sources of
systematic risk. Economic, political and sociological changes are sources of systematic
risk.
Systematic risk further divided into
-Market Risk
-Interest
-Purchasing power Risk

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Market Risk
J.C. Francis defined Market risk as that portion of total variability of returned
caused by the alternating farces of bull and bear market. When the security index moves
upwards haltingly for a significant period of time, it is known as bull market. In the bull
market the indeed moves form a low level to the peak. Bear market is just reverse to the
bull market. During the bull and bear market more than 80 percent of the securities prices
rise or fall along with the stock market indices.
Interest Rate Risk
The rise or fall in the interest rate affects the cost borrowing. When the call
money market rate changes. Interest rates not only affect the security traders but also
corporate bodies who carry their business on borrowed funds. The cost of borrowing
would.
Increase and a heavy out flow of profit would take place in the form of interest to
the capital borrowed. This lead a reduction in earning per share and a consequent fall in
the price of share.
Purchasing power Risk
Variations in the returns are caused also by the loss of purchasing power of
currency. Inflation is the reason behind the loss of purchasing power the rise in price
penalizes the returns to the investors, and every potential rise in price a risk to the
investor.

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Unsystematic Risk
Unsystematic risk is the unique risk, which will be different to different firms.
Unsystematic risk stems form managerial inefficiency, technological change in
production process, availability of raw material mentioned factors differ form industry to
industry, and company to company. They have to be analyzed separately for each
industry and firm.
Broadly Unsystematic risk can be classified into:
-Business risk
-Financial risk
Business Risk
It is the portion of the unsystematic risk caused by the operat6in environment of
the business.
Financial Risk
Financial risk in a company is associated with the capital structure the company.
It refers to the variability of the income to the equity capital to debt capital.
Measurement of Risk
The risk of a portfolio can be measured by using the following measure of risk
Variability
Investment risk is associated with the variability of rates of return. The more
variable is the return, the more risky the investment. The total variance is the rate of

36. GARGIRAI Page 36
return on a stock around the expected average, which includes both systematic and
unsystematic risk.
The total risk can be calculated by using the standard deviation. The standard
deviation of a set of numbers is the squares root of the square of deviation around the
arithmetic average.
Ymbolically, the standard deviation can be expressed as-
ð = ∑ (rit-ri)
n-1
Where,
ri is the mean return of the portfolio and
rit is the return form the portfolio for a particular year

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SHARPE’S PERFORMANCE INDEX:-
William Sharpe’s of portfolio performance is also known as reward to variability
ratio (RVAR). It is simply the ratio of reward, which defined as realized portfolio returns
in excess of the risk free rate, to the variability of return measured by the standard
deviation relation to total risk assumed by the investor.
The measure can be defined follows:-
RVAR = rp-rf
ð
Where,
rp= the average return for the portfolio (P) during it HPR
rf= risk free rate of return during JHPR
ð = the standard deviation of the portfolio (P) during HPR

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CAPITAL MARKET LINE
Capital market shows the conditions prevailing in the capital market in terms of
expected return and risk. It depicts the equilibrium condition that prevails in the market
for efficient portfolio’s consisting of the portfolio of risky asset or risk free asset or both.
All combination of risky and risk free portfolio are bounded by the capital market line,
and all investors will end up with portfolio somewhere on the capital market line. The
capital market is usually derived under the assumptions that there exists a risk a risk-less
asset available for investment. It is further assumed that6 investor can borrow or lend as
much as desired at the risk free assets with a portfolio or risky assets to obtain the desired
risk return combination. Using the capital market line can graphically represent Sharpe’s
measure for portfolios. The vertical axis represents the return on the portfolios and the the
horizontal axis represents the standard deviation for returns. The vertical intercept is rf.
RVAR measures the slope of the line form rf to the portfolio being evaluated. The steeper
the line, the higher the slope (RVAR) and the better performance.

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TREYNOR’S PERFORMANCE INDEX
The measure is also referred to as reward to volatility ratios (RVOL). Treynor
sough to relate return on a portfolio to its risk. He distinguished between total risk and
systematic risk assuming that6 the portfolio is well diversified. In measuring the portfolio
performance Treynor introduced the concept of characteristic line. The slope of the
characteristics measures the relative volatility of the portfolio’s returns. The slope of this
line is the beta co-efficient which is measure of the volatility (or responsiveness) of the
portfolio’s returns in relation to those of the market index. Treynors’s ratio is the realized
portfolio’s return in excess of the risk-free to the volatility of return as measured by the
portfolio beta.
RVOT = rp-rf
Bp
= Average excess return of portfolio (P)
Systematic risk for portfolio

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SECURITY MAEKET LINE
The security market line indicates the risk-return trade-off for portfolio and
individual securities. Treynor extended his analysis to identify the component of risk
that will be compensated by the market. It is known as systematic risk and is commonly
measured by the beta. Beta is a measure of risk that applies to all assets and portfolio
whether efficient or inefficient. Security market line specifies the relationship between
expected return and risk for all assets and portfolios whether efficient or inefficient. The
security market is obtained by taking the risk (beta) on the horizontal axis and portfolio
return on the vertical axis. The Security market line can be graphically.
E (rm) SML
rf
Beta 1.00

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Beta
Beta is a market risk measure employed primarily in the equity. It measures the
systematic risk of a single instrument or an entire portfolio. William Sharp (1964) used
the notion in his landmark paper introducing the capital asset pricing model (CAPM).
The name “beta” was applied later.
Beta describes the sensitivity of an instrument or portfolio to broad market
movements. The stock market (represented by an index such s the S&P 500 or 100) is
assigned a beta of 1.0. By comparison, a portfolio (or instrument) with a beta of 2.0 will
tend to benefit or suffer form broad market moves twice as much as the market overall.
The formula for beta is
β = ∑XY-(∑XY) (∑Y)
N∑X-(∑X)
Where X is the market return
And Y is the security return
Both quantities are calculated using simple returns. Beta is generally estimated
form historical price time series. For example, 60 trading of simple returns might be used
with sample estimators for covariance and variance.
It is possible to construct negative beta portfolio beta portfolios. Approaches include.
Beta is sometimes used as a measure of a portfolio’s mark risk. This can be misleading
because beta does not capture specific risk. Because of specific risk. A portfolio can have
a low beta, but still be highly volatile. Ti price fluctuations would simply have a low
correlation with those of the overall market. It is said that a security or portfolio having
higher beta will perform well provided market has to go up i.e., market indeed

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Calculation of standard deviation of returns
PORTFOLIO I
Year Return Di=r-ri Di*Di S.D
2005 27.85 -13.273 176.18
2006 1.02 -40.103 1608.3 48.133
2007 94.5 53.377 2849.1
Ri= 41.123 4633.5

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PORTFOLIO II
Year Return Di=r-ri Di*Di S.D
2005 18.26 -18.867 355.95
2006 -5.98 -43.973 1858.2 55.022
2007 99.1 3840.7
Ri= 37.127 6054.8

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PORTFOLIO III
Year Return Di=r-ri Di*Di S.D
2005 45.54 -8.0267 64.427
2006 13.99 -39.577 1566.3 44.141
2007 101.17 47.603 2266.1
Ri= 53.567 3896.8

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SHARPE PERFORMANCE MEASURE
Portfolios
Avg
portfolio
Return
(;p) in %
Risk free
Rate
(n)%
Excess
return
(rp-ri)
Standard
Deviation
Sharpe’s
Ratio rp-
rt
Ranking
I 41.128 5.25 35.878 48.13 0.745 2
II 37.128 5.25 31.878 55.02 0.579 3
III 52.57 5.25 47.32 44.14 1.072 1

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TREYNOR’S PERFORMANCE MEASURE CALCULATION OF BETA
Beta for portfolio I
Year Avg
Market
Return X
X2
Avg
Stock
Return Y
XY
2004-05 5.683 32.296 27.855 158.3
2005-06 -8.827 77.916 1.025 -9.0477
2006-07 72.886 5890.8 123.38 7334.4
Beta =1.05261

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Beta portfolio II
Year Avg
Market
Return X
X2
Avg
Stock
Return Y
XY
2004-05 5.683 32.296 18.267 103.81
2005-06 -8.827 77.916 -5.985 52.83
2006-07 76.03 5780.6 99.102 7534.7
72.886 5890.8 111.38 7691.4
Beta =1.210018

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Beta for portfolio III
Beta =0.965732
Year Avg
Market
Return X
X2
Avg
Stock
Return Y
XY
2004-05 5.683 32.296 42.548 241.8
2005-06 -8.827 77.916 13.99 -123.49
2006-07 76.03 5780.6 101.17 7692.1
72.886 5890.8 157.71 7810.4

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TREYNORS PERFOMANCE INDEDX
Portfolios
Portfolio
Avg
Return
(rp)
Risk free
Rate (rf)
Beta Risk
Premimum
Tn
Rp-rf
ß
Ranking
I 41.128 5.25 1.052 35.878 34.1046 2
II 37.128 5.25 1.21 31.878 26.3455 3
III 52.57 5.25 0.965 47.32 49.0363 1

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PART C

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ANALYSIS
AND
INTERPRETATIONS

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HOLDING PERIOD RETURNS
In THE YEAR 2004 NSE INDEX gained 5.58% returns during the same year
portfolio I, II and III has registered a growth of 27.85, 94.50 respectively. Return wise
portfolio III emerges as best portfolio subsequently PI and PII
During the year 2005 the NSE INDEX registered a negative growth rate of -8.82
during the same year portfolio I II and III has registered return of 18.26, -5.98 and 99.10
respectively. Return wise portfolio III performs well and portfolio I and II occupying
subsequent position.
In the year 2006 he NSE INDEX shows a fabulous growth rate of 76.88 and
portfolio I, II and III performed by 42.54, 13.29 and 101.17 and portfolio III emerged as
best portfolio subsequently portfolio I and II

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OVERALL PERFOMANCE
The overall performance of the market and the portfolios can be shown by taking
the arithmetic average of return. For the previously said of three years market has
registered growth rate of 24.58. Arithmetic of portfolio I II and III are 41.128, 37.12 and
52.57 respectively. Portfolio III emerges as best performer.

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SHARPE’S PERFORMANCEMEASURE
Sharpe’s performance measure gives the appropriate return per unit of risk as
measured by standard deviation. The reward of variability ratios computed has shown the
ex-post return of per unit of risk for the three portfolio’s for the period of three years.
The rate of risk of portfolio II is high deviation by 55.02 by an average return of
37.12, similarly the portfolio I has a deviation of 48.13 with a return or 41.128 and
portfolio III with a deviation of 44.14 with an average return of 55.57.
Using 5.25 as return on saving bank account as a proxy for the risk free rate and
substuting there value in Sharpe’s evaluation portfolio I gives a slope of 0.745, in
portfolio I gives a reward of 35.87(41.128-4.25) for bearing a risk of 48.13 making the
sharpe’s ratio to 0.745. For every additional 1% risk and investor has as additional pf
0.745 returns for above portfolio.
Portfolio II gives a return or 37.12 while the standard deviation was 55.02 using
5% return on the saving account as proxy market shares ratios to 0.579. Therefore for
every additional 1% risk investor will earn an additional 0.579 of return. And portfolio II
with a return of 52.57 with an standard deviation making Sharpes ratios to 1.072 as
additional return.

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OVERALLPERFORMANCE
Overall performances of the portfolios are 41.12, 37, 12 and 52.57 respectively.
The risk free rate was 5.25. Investing in three portfolios during the same period provide
an risk premium of 35.87, 31.87, one 47.32 respectively. For every 1% of additional risk
an investor will earn 0.745, 0.579 and 1.07 of return. Portfolio III outperformed by 1.072
compared with other two portfolios. The investor will earn on return per unit of beta of
34.120, 26.34 and 49.036 by ranking the portfolio shows that portfolio III performs well
as compared with other two portfolios.

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TREYNOR’SPERFORMANCEMEASURE
Treynor’s performance measure gives appropriate return per unit or firsk as
measured by the beta coefficient.
Portfolio I,II and II provided a return of 41.12% 37.12% and 52.57% with 1.05%
1.21% and 0.965% as beta coefficient respectively. Treynor’s ratios for the three
portfolios above the risk free rate of 5.25% were 34.16%26.34%, 49.036% respectively.
Investing in portfolio I II and III provides risk premium of 35.87, 31.87 and47.32 for
bearing a risk of beta of 1.052% 1.21% and 0.965% receptively. Thus an investor will
earn a return per unit of beta of 34.16% 26.34% and 49.03% receptively. Portfolio III
emerging as the best performer, portfolio I and II was occupying the subsequent position.

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CONCLUSIONSAND SUGGESTIONS
1. Among the three portfolios I II and III, portfolio III gives a highest return with a
proportionate risk ( ) of 44% with a return of 52.57%.
2. Portfolio III has outperformed in both sharpe’s and Treynor’s measure.
3. It is advisable to invest in portfolio III i.e. foreign collaboration securities in long
run and portfolio II i.e. public limited companies in short run because the later is
more correlated with the market index.
4. Diversification of portfolios in various projects or securities may reduce high risk
and it provides the high wealth to the shareholders.
5. Beta is used to evaluate the risk proper measurement of beta may reduce the high
risk and it gives the high risk premium.

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BIBLIOGRAPHY

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BIBLIOGRAPHY
 Prasanna Chandra (Security Analysis and Portfolio Management)
 Avadhani (Security Analysis and Portfolio Management)
 Francis and Taylor (Investment Management)
 Graham and Dodd Security Analysis, McGraw Hill

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